Levenberg–Marquardt algorithm: Difference between revisions

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== The problem ==
 
Given are ''m'' functions ''f''<sub>1</sub>, ..., ''f''<sub>''m''</sub> of ''n'' parameters ''p''<sub>1</sub>, ..., ''p''<sub>''n''</sub> with ''m''&ge;''n''. It is convenient to use vector notation for both the functions and the parameters,
:'''f'''<sup>T</sup>=(''f''<sub>1</sub>, ..., ''f''<sub>''m''</sub>), and '''p'''<sup>T</sup>=(''p''<sub>1</sub>, ..., ''p''<sub>''n''</sub>).
The least squares problem consists in finding the parameter vector '''p''' for which the cost function